Question

name
olexia smoot
hour 6th //14/20
4.1 reflections · spiral review
graph the image of each figure under the given reflection. determine the coordinates of the image.

1. △abc in the line y = x
2. trapezoid defg in the line x = -1
3. parallelogram rstu in the line y = x
4. square klmn in the line y = -2

Explanation:

Step1: Identify the figure (parallelogram RSTU)

Locate the vertices of parallelogram RSTU on the coordinate grid. Let's assume the coordinates (we'll estimate from the grid):

• Let’s find coordinates of R, S, T, U. From the grid, suppose:
• R: Let's say R is at (2, 3) (estimating from the grid lines, O is origin (0,0), so moving right 2, up 3)
• S: (3, 1) (right 3, up 1)
• T: (-2, 1) (left 2, up 1)
• U: (-3, 3) (left 3, up 3)

Step2: Recall reflection over \( y = x \) rule

The rule for reflecting a point \((x, y)\) over the line \( y = x \) is \((x, y) \to (y, x)\).

Step3: Apply the rule to each vertex

• For R \((2, 3)\): Reflect to \((3, 2)\)
• For S \((3, 1)\): Reflect to \((1, 3)\)
• For T \((-2, 1)\): Reflect to \((1, -2)\)
• For U \((-3, 3)\): Reflect to \((3, -3)\)

Step4: Plot the reflected points

Plot \((3, 2)\), \((1, 3)\), \((1, -2)\), \((3, -3)\) on the grid and connect them to form the reflected parallelogram.

(Note: If exact coordinates were given, we'd use them, but since we estimate from the grid, the key is applying the reflection rule \( (x,y) \to (y,x) \) to each vertex of RSTU.)

Answer:

To graph the reflection of parallelogram RSTU over \( y = x \), reflect each vertex \((x, y)\) to \((y, x)\), then plot and connect the new vertices. (The specific coordinates depend on the exact grid positions, but the process uses the reflection rule \( (x,y) \to (y,x) \).)